Question

1/2x+1/5y=1/15;1/2x+3y=1/12 solve this simultenous equation
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Answer 1

Answer:1/3x + 1/5y = 1/15

Multiplying the equation by 15 on both the sides we get,

5/x + 3/y = 1

1/2x + 1/3y = 1/12

Multiplying the equation by 12 on both the sides we get,

6/x + 4/y = 1

Now,

Let 1/x = a and 1/y = b

∴ We get, 5a + 3b = 1 ......... eq. no. (1)

and 6a + 4b = 1 ........ eq. no. (2)

Multiplying (1) bt 4, we get

20a + 12b = 4 .........(3)

Multiplying (2) by 3, we get

18a + 12b = 3 ........(vi)

Subtracting  (4) from (3),

20a

+12b

=

4

18a

+12b

=

3

(-)

(-)

(-)

2a

=

1

∴ a = 1/2

Substituting a = 1/2  in equation (2)

∴ 6a + 4b = 1

∴ 6(1/2) + 4b = 1

∴ 3 + 4b = 1

∴ 4b = 1 – 3

∴ 4b = - 2

∴ b= - 2 /4

∴ b = -1/2

Substituting the values of a and b,

a = 1/2

∴ 1/x = 1/2

∴ x = 2

b = -1/2

∴ 1/y = -1/2

∴ y = -2

∴ x = 2  and y = - 2 is the solution of given simultaneous equations.

Explanation: